Simulation of Mussel Mytilus Galloprovincialis Growth with a Dynamic Energy Budget Model in Maliakos and Thermaikos Gulfs (Eastern Mediterranean)

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Vol. 9: 371–383, 2017 AQUACULTURE ENVIRONMENT INTERACTIONS Published September 28 https://doi.org/10.3354/aei00236 Aquacult Environ Interact

OPENPEN ACCESSCCESS Simulation of mussel Mytilus galloprovincialis growth with a dynamic energy budget model in Maliakos and Thermaikos Gulfs (Eastern Mediterranean)

Yannis Hatzonikolakis1,2, Kostas Tsiaras2, John A. Theodorou3, George Petihakis4, Sarantis Sofianos1, George Triantafyllou2,*

1Department of Environmental Physics, University of Athens, 15784 Athens, Greece 2Hellenic Centre for Marine Research (HCMR), Athens-Sounio Avenue, Mavro Lithari, 19013 Anavyssos, Greece 3Department of Fisheries and Aquaculture Technology, Technological Educational Institute of Western Greece, Nea Ktiria, Mesolonghi 30200, Greece 4Hellenic Centre for Marine Research (HCMR), 71003 Heraklion, Greece

ABSTRACT: A dynamic energy budget (DEB) model was developed to investigate the growth and reproduction of cultured bivalve species raised under different environmental conditions (varying phytoplankton carbon biomass [Phyto-C], particulate organic carbon [POC] and temperature) and tuned against field data for Mytilus galloprovincialis from the Maliakos and Thermaikos Gulfs (Aegean Sea, Greece). Values of most DEB model parameters were adopted from the literature, while half saturation constant (Xk) and initial values of energy reserves (E) and reproductive buffer (R) were calibrated. Different values have been found for Xk in the 2 areas (Maliakos: Xk = −3 −3 36 mg C m ; Thermaikos: Xk = 28 mg C m ), suggesting that Xk should be treated as a site-specific parameter. Food density (X) was adapted to include not only Phyto-C but also POC in the diet of M. galloprovincialis and only when Phyto-C density was low compared to POC density. Results showed a small contribution of POC during spring in the Maliakos Gulf and almost none at Ther- maikos Gulf. The simulated mussel growth showed good agreement with field data. Sensitivity tests on the calibrated parameters (E, R and Xk) were performed to investigate model uncertainty. The standard deviation of simulations with perturbed parameter/initial values remained relatively small and appeared to increase as the modeled mussel grew, in agreement with observations.

KEY WORDS: Dynamic energy budget · DEB model · Mussel culture · Mytilus galloprovincialis · Growth · Eastern Mediterranean · Uncertainty · Ensemble forecasting

INTRODUCTION this aquaculture production comes from shellfish farms. For example, in Europe in 2009, 57% of total According to the Food and Agriculture Organization aquaculture production came from mussel, clam and of the United Nations (FAO), the world’s population oyster farming (Eurostat 2016). Considering that shell- will reach 8 billion people in 2030. This increase is not fish farming takes place in coastal zones which are af- reflected in wild fisheries or oyster production, which fected both by anthropogenic pressures and climate have been practically steady since 1989. On the other change, it is important to analyze and understand the hand, world aquaculture production has shown an processes that affect production. Among the most im- enormous growth in the last 3 decades, increasing portant cultured bivalve species is the Mediterranean from 14% of total seafood production in 1988 to mussel Mytilus galloprovincialis , which has significant 44.1% in 2014 (FAO 2016). A significant amount of global production (116 262 metric tonnes [t] in 2014

© The authors 2017. Open Access under Creative Commons by *Corresponding author: [email protected] Attribution Licence. Use, distribution and reproduction are un - restricted. Authors and original publication must be credited. Publisher: Inter-Research · www.int-res.com 372 Aquacult Environ Interact 9: 371–383, 2017

according to FAO1) and is mainly cultured on the al. 2010, Handa et al. 2011, Thomas et al. 2011, Wijs- northern shores of the Mediterranean Sea (Rodrigues man & Smaal 2011, Sarà et al. 2012, among others). et al. 2015). Greece contributes significantly to Medi- DEB models show important benefits in describing terranean M. galloprovincialis farming, with an esti- the growth of an individual organism and have the mated maximum farming carrying capacity up to powerful aspect of being generic: DEB theory 35 000 or 40 000 t gross weight (although production assumptions represent physiological processes that levels are currently lower: 18 000 t in 2014; FGM 2015). are common among different species, with their dif- Because of the overall oligotrophic characteristics of ferences reflected only in the values of the parame- the Mediterranean, major farming areas are only ters. Moreover, DEB models can be used as a basis found close to estuarine systems. In Greece, these are for modeling other processes, e.g. concentrations of mainly located in the northern part of the country contaminants in an individual (Zaldívar 2008) or where major rivers discharge (Theodorou et al. 2011, bioaccumulation of trace metals (Casas & Bacher 2015a), and are more scattered in other areas of conti- 2006). Larsen et al. (2014) compared the results of nental Greece (Fig. 1). bio-energetic growth (BEG), scope for growth (SFG) In the present study, the growth of M. galloprovin- and DEB models on growth data of blue mussels from cialis in the Maliakos and Thermaikos Gulfs was in- Danish waters, and concluded that the DEB model vestigated. A model describing the growth of M. gal- provided the best results and predictions regarding loprovincialis was developed based on dynamic mussel somatic growth. Brigolin et al. (2009) chose a energy budget (DEB) theory (Kooijman 1986, 2000). model based on the dynamic estimation of SFG as The model simulates the growth of an individual cul- being more appropriate to study nutrient, carbon tured mussel, assuming that the simulated individual and phosphorus fluxes related to ingestion and the represents the average state of the farm’s population. production of feces and pseudofeces in M. gallo- DEB models have been applied successfully for sev- provincialis. In their study, they also compared the eral bivalve species (Casas & Bacher 2006, Pouvreau results between their model and the DEB model pro- et al. 2006, Zaldívar 2008, Bourlès et al. 2009, Troost et duced by Casas & Bacher (2006), concluding that both models can give good simulations regarding the 1China and Spain mussel production is not reported as somatic growth of M. galloprovincialis. Mytilus galloprovincialis production by FAO The primary objective of this work was to develop a model describing the growth and reproduction of the Medi- terranean mussel M. galloprovincialis that can be used to investigate processes affecting production on shellfish farms, offering a useful tool for the study of mussel farming in the Maliakos and Thermaikos Gulfs and estimating the carrying capacity of the study areas.

MATERIALS AND METHODS

Study area and mussel growth data

Maliakos Gulf is a semi-enclosed, shallow (14 m mean depth) estuarine embayment in the central western part of the Aegean Sea which covers a total surface of 110 km2. It receives fresh water discharge from the Spercheios River at an average rate of 68 m3 s−1; Fig. 1. Mussel farms (black circles) in Greece, Eastern Mediterranean. Num- there is also some inflow of more saline bers of floating longlines (no. of hanging parks in brackets) in the area are indicated. (*) Licensed but not yet active longlines. Study areas (Thermaikos and water from the N. Evoikos Gulf through Maliakos Gulfs) are indicated (adapted from Theodorou et al. 2011, 2015a) an anti-clockwise circulation in the Hatzonikolakis et al.: DEB mussel model 373

north ern part of the gulf (Christou et al. 1995). Mus- chlorophyll a (chl a) and temperature. Phyto-C was sel farming was established in late 1980s, and today obtained from chl a data, assuming a constant car- there are 10 farms with an estimated total annual bon:chl a ratio (50:1) that can be considered as a production of around 1500 to 1700 t yr−1 (Dimitriou et mean value of ratio’s seasonal variability (Malone & al. 2015, Theodorou et al. 2015b). Chervin 1979, Geider & Piatt 1986, Kormas et al. Monthly mussel growth data (i.e. fresh tissue mass 2002). These datasets were used to force the model, [g] and shell length [cm]) were derived from a farm and their values at each model time step were (CalypsoSeafood/Aqua-Consulting) in the area of obtained by linear interpolation from the monthly Molos (Southern Maliakos). Specifically, 3 pergolar- data. Particulate organic carbon (POC) used in model ies (mussel ‘socks’ made of plastic cylindrical nets) simulations was obtained from Kormas et al. (2002). 3 m in length were filled with mussel seed (n = 30) of In Thermaikos Gulf, input data (temperature, Phyto- average (±SD) length (3.68 ± 0.53 cm) and weight C, POC) for the period during which mussel growth (1.43 ± 0.21 g). The pergolaries were attached to a data were available (May 1995 to July 1996) were ob- ‘mother’ longline rope at the edge of the farm in Sep- tained from a 3-dimensional (3-D) hydrodynamic/bio- tember 2004. To estimate animal growth, on a chemical long-term model simulation over the 1980 to monthly basis 30 to 40 mussels were randomly col- 2000 period (Tsiaras et al. 2014). The hydrodynamic lected from this batch for morphometric analysis dur- model was based on the Princeton Ocean Model ing the period from October 2004 to June 2005. (POM; Blumberg & Mellor 1983) while the biochemi- Thermaikos Gulf is a semi-enclosed basin with a cal model was based on the European Regional Seas total surface area of 5100 km2, located in the north- Ecosystem Model (ERSEM; Baretta et al. 1995). The 3- west Aegean. Depth varies from 10 to 75 m and the D model results were validated against available Sea- tidal range is 0.25 m. The inner Thermaikos Gulf is WiFS chl a and in situ data (Tsiaras et al. 2014). one of the few areas in Greece that can be character- The 2 coastal environments show some differences, ized as eutrophic (Pagou 2005, Papakonstantinou et mostly related to the maximum values and variability al. 2007), and contains one of the most extensive and of Phyto-C. In Maliakos Gulf, Phyto-C reaches its productive mussel aquacultures, reaching 90% of highest value in winter (277 mg C m−3), when the total production in Greece (Konstantinou et al. 2015). phytoplankton bloom takes place. This bloom is at- Mussel growth data, provided by Kravva (2000) tributed to the supply of nutrients from Sperchios from the coastal area of Chalastra, were used for tun- River in the early winter and is characterized by rapid ing the Thermaikos Gulf model. This area is in - sedimentation of phytoplankton cells to the shallow fluenced by 2 of the most important rivers (Axios, seafloor (Kormas et al. 1998). In Thermaikos Gulf Aliakmon) in the northern Aegean. It receives sig - (Chalastra), Phyto-C peaks in late April with a value nificant inputs of particulate matter and dissolved of 138 mg C m−3. Although Phyto-C in Maliakos constituents (Price et al. 2005), creating favorable Gulf exhibits a significantly higher peak compared to conditions for phytoplankton growth and thus is an Thermaikos, the annual mean values are similar in ideal area for the cultivation of mussels. the 2 areas (Maliakos: 94.5 mg C m−3; Thermaikos: 90 mg C m−3). In Maliakos Gulf, Phyto-C was high throughout August 2004 to February 2005, but after- Environmental data ward decreased to very low levels between March 2005 and August 2005. Phyto-C in Thermaikos Gulf Near-surface temperature and phytoplankton car- showed more moderate fluctuations. This can be bon biomass (Phyto-C) data (Fig. 2) were used as attributed to the fact that the 3-D hydrodynamic/ forcing functions for the DEB mussel model imple- biochemical model of Thermaikos Gulf adopts a cli- mentations in the Maliakos and Thermaikos Gulfs. matologic seasonal variability for river discharge and Data provided for Maliakos (August 2004 to August therefore cannot capture high-frequency variability. 2005) are outcomes of the Project ARCHIMIDES I −EPEAEK II-EU (contract no. 10012-00004) ‘Environ- mental Interactions of the Mussel farming’ (2004- DEB model 2007). Relevant data used in the present study are from the deliverables of this effort presented in Description of the DEB mussel model Theodorou et al. (2006a,b 2007) and Kakali et al. (2006). Monthly data samples at 4 depths (0.5, 2, 3 The basic assumption of a DEB model is that the and 6 m) were used to calculate mean near-surface assimilated food first enters a reserve pool and then is 374 Aquacult Environ Interact 9: 371–383, 2017

25 Maliakos 20 Thermaikos

(°C) 15 10

Temperature Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul )

–3 300 200 100 Phyto-C (mg C m Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul )

–3 400

200 POC (mg C m Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul

Fig. 2. Environmental data used for the forcing of the dynamic energy budget model in the Maliakos (black line) and Ther- maikos (blue line) Gulf simulations, showing temperature (top), phytoplankton carbon biomass (middle), and particulate organic carbon (bottom) allocated between the other compartments: a fixed was tuned in the current study in order to obtain a part, κ, is spent on somatic maintenance and growth, better fit of model-simulated growth with observa- while the remaining, 1 − κ, on maturity maintenance tions. Widdows et al. (1984) and later Camacho et al. and reproduction. This rule is known as the κ-rule. (1995) showed that the differences in physiological The individual is characterized by 3 state variables: re sponses among populations, which are mainly structural volume V (cm3), energy reserves E (joules) Table 1. Dynamic energy budget model: equations. See and energy allocated to development and reproduc- Table 2 for model variables, Table 3 for parameters and tion R (joules), while the environment of the indi - Table 4 for initial values vidual is described by food density and temperature. All model equations describing the time evolution dE  (1) = ppac− of feeding, maintenance, growth, development and dt dV κ⋅ppV −[] ⋅ reproduction are shown in Table 1; descriptions of = cM (2) model variables are provided in Table 2. The inter- dt []Eg ested reader may refer to Zaldívar (2008) and Casas dR = (1−⋅kp ) − [1−κ ] ⋅ min ( VVp , ) ⋅ [ ] (3) & Bacher (2006) for a full description of the model dt c κ pM equations.  2/3 ppfkTVaAm= {}⋅⋅ () ⋅ (4) X f = (5) Parameter values XX+ k  2/3  []E ⎛ []{}()EpgAM⋅⋅⋅ kTV  ⎞ pc = ⋅⎜ + [] pV M ⋅ ⎟ (6) Most of the model parameters used in the present []EEg + κ⋅ []⎝ []Em ⎠ study for Mytilus galloprovincialis are adapted from E (7) those estimated by Van der Veer et al. (2006) for the []E = V blue mussel M. edulis L. in the northeast Atlantic  (8) (see Table 3 for exceptions). Τhe 2 mussel species are []pkTpMMm= ()[]⋅ closely related and are very similar ‘with no single morphological or genetic character being clearly exp()TA − TA kT()= TI T (9) diagnostic’ (Gosling 1984, p. 554). Preliminary exper- TALT AL TAH TAH 1+ exp()()T − T + exp T − T imentation showed that this specific parameteriza- L H tion resulted in good agreement of M. galloprovin- V 1/3 L = cialis model-simulated growth with observations. A δm (10) similar approach was used by Casas & Bacher (2006) ⎛ E ⎞ R WdV= ⋅⎜ + ⎟ + (11) for M. gal loprovincialis along the French Mediter- ⎝ []Eg ⎠ μE ranean shoreline. The half-saturation coefficient (Xk) Hatzonikolakis et al.: DEB mussel model 375

Table 2. Dynamic energy budget model: variables lower value in less productive areas, such as the Aegean coastal areas. Specific density (d) was set to Variable Description Units 1 g cm−3 as suggested by Kooijman (2000). The values of all DEB model parameters used are summa- V Structural volume cm3 rized in Table 3. E Energy reserves J R Energy allocated to development J and reproduction · −1 pa Assimilation energy rate J d Initial values · −1 pc Energy utilization rate J d f Functional response function − The initial values used for each simulation run are −3 X Food density mg C m shown in Table 4. For both study areas, the initial []p −3 −1 M Maintenance costs J cm d value of shell length (L) was set from the field T Temperature K data, while initial V was calculated from Eq. (10) (see k(T) Temperature dependence − Table 1). For the Thermaikos simulation, initial R was L Shell length cm W Fresh tissue mass g chosen to be 0; the initial mussel body volume, V, in- dicates that the individual is in the juvenile phase (V <

Vp; see Table 3) and thus it was assumed that the ani- responsible for differences in growth rate, are mainly mal has no energy allocated for reproduction yet, fol- the result of environmental conditions and to a lesser lowing the same approach as Thomas et al. (2011). In extent, genetic differences. Therefore, a good mo - Maliakos Gulf, the initial V, obtained from the field deling approach would be to capture the differences data, suggests that the individual is mature and thus in phy siological responses among the 2 similar some energy has to be allocated for reproduction (R). species and populations (Hilbish et al. 1994, Fly & In the absence of available data, a model simulation

Hilbish 2013) by the site-specific parameter, Xk initialized as in the Thermaikos Gulf (V < Vp and R = (Troost et. al. 2010). Xk is the amount of food (Phyto- 0) was used to estimate the initial R at the observed C, POC) where food uptake is at half its maximum mussel length (L = 3.68 cm) and weight (W = 1.43 g) at value (see ‘Food density’ below) and may be consid- Maliakos. For both study areas, the initial value of E ered representative of the environment to which the was calibrated (Table 4), so that the computed initial organism has adapted. A higher value of Xk is thus W (Eq. 11) shows the best fit with field data. Re- expected in more productive environments, such as garding initial allocation between E and R, Rosland the French Mediterranean shoreline as in Casas & et al. (2009) performed sensitivity experiments and −1 −3 Bacher (2006) (Xk = 3.88 µg l ; ~194 mg C m ) and a demonstrated that it has little impact on the results.

Table 3. Dynamic energy budget model: parameters

Parameter Units Description Value Reference

 −2 −1 {}pAm J cm d Maximum surface area-specific assimilation rate 147.6 Van der Veer et al. (2006) −3 Xk mg C m Half saturation coefficient Calibrated −

TA K Arrhenius temperature 5800 Van der Veer et al. (2006)

TI K Reference temperature 293 Van der Veer et al. (2006)

TL K Lower boundary of tolerance rate 275 Van der Veer et al. (2006)

TH K Upper boundary of tolerance rate 296 Van der Veer et al. (2006)

TAL K Rate of decrease of lower boundary 45 430 Van der Veer et al. (2006)

TAH K Rate of decrease of upper boundary 31 376 Van der Veer et al. (2006)  −3 −1 []pM m J cm d Volume specific maintenance costs 24 Van der Veer et al. (2006) −3 [EG]J cmVolume specific costs of growth 1900 Van der Veer et al. (2006) −3 [Em]J cmMaximum energy density 2190 Van der Veer et al. (2006) κ − Fraction of utilized energy spent on maintenance/growth 0.7 Van der Veer et al. (2006) 3 Vp cm Volume at start of reproductive stage 0.06 Van der Veer et al. (2006)

δm − Shape coefficient 0.25 Casas & Bacher (2006) d g cm−3 Specific density 1.0 Kooijman (2000) −1 μΕ J g Energy content of reserves 6750 Casas & Bacher (2006) 376 Aquacult Environ Interact 9: 371–383, 2017

Table 4. Dynamic energy budget model: initial values. L: [Phyto–C] shell length; W: fresh tissue mass; V: structural volume; E: aa= f ⋅ (13) [Phyto–C]+ X energy reserves; R: energy allocated to development and k reproduction [POC] bb= f ⋅ (14) [POC]+ X k Maliakos Gulf Thermaikos Gulf Variable Value Variable Value where [Phyto-C] is the density of available Phyto-C and [POC] is the density of available POC. Parame-

Start date 28 Sep 2004 Start date 15 May 1995 ters af and b f describe the mussels’ relative prefer- L 3.68 cm L 0.84 cm ence for Phyto-C and POC, which is related to food W 1.43 g W 0.054 g V 0.7787 cm3 V 0.0093 cm3 quality. Troost et al. (2010) investigated the impor- E 700 J E 350 J tance of detritus as a food source between different R 300 J R 0 J shellfish species and concluded that the contribution of detritus to shellfish’s diet might differ among different environments. For example, cockles prefer phytoplankton as a food source but in those areas This conclusion has been verified with the method of where phytoplankton concentrations are low, cockles Rosland et al. (2009) on preliminary tests. Allocating can also assimilate detritus (Troost et al. 2010). To all initial energy to E increased final L by 0.87% and simulate this behavior, variable preference weights final W by 2.84%. Allocating all initial energy to R (a, b) were adopted, depending on the availability of decreased final L by 2.18% and W by 6.32%. food resources in terms of Phyto-C and POC, as given by Eqs. (13) & (14). In this way, the contribution of POC will be significant only when Phyto-C is low Simulation of reproduction compared to POC density. The seasonal contribution of POC for M. galloprovincialis is discussed below.

To simulate the loss of mussel weight at spawning Parameters af and bf were determined by calibration: (Van Haren et al. 1994), the buffer R was completely af = 0.55, and bf = 0.45 (see ‘Discussion’ for more emptied (R = 0) on the spawning day, which was set details regarding these values). at the time of the year when the field data and literature indicate that spawning events occur. The same method was applied by Handa et al. (2011) and Simulation of starvation Zaldívar (2008). Spawning events for M. galloprovincialis in Maliakos and Thermaikos Gulfs occur Following Rosland et al. (2009) and Handa et al. between December and March (Fasoulas & Fantidou (2011), when the growth rate according to Eq. (2) is 2008, Theodorou et al. 2011). Thus, for the simulated negative, it is assumed that the energy utilization mussel individual the spawning day was set at about rate is not enough to cover somatic maintenance. In the middle of the spawning season. this case, the mussel is assumed to be in a starvation state and stops growing (dV/dt is set to 0). Energy is also withdrawn from the reproductive buffer to cover Food density the maintenance deficit, following Handa et al. (2011); thus the reproduction equation changes to: The relation between food uptake and food density dR  (15) is described by a Holling Type II (Holling 1959) func- = κ⋅ppcM − dt tional response, f (Eq. 5), which can vary between 0 and 1. As a first approach, only Phyto-C was considered in the food density (X): X = [Phyto-C]. As a sec- RESULTS ond method, the functional response was adjusted to include not only Phyto-C but also POC in the simu- Model simulation lated mussel diet. In this case, the food density X is given by: Simulations of the growth of Mytilus galloprovincialis for the same period as the experimental data ab⋅[Phyto-C]+ ⋅ [POC] X = (12) were performed first with food density X = [Phyto-C]. ab ff+ Results are shown in Fig. 3 for Maliakos Gulf and where a and b are given by: Fig. 4 for Thermaikos Gulf. Xk was tuned to different Hatzonikolakis et al.: DEB mussel model 377

8 To achieve a more realistic simulation of mussel growth, POC was 6 added to the diet of M. galloprovin- (cm)

L 4 cialis, with food function, X, given by Eq. (12). In Figs. 3 & 4, the 2 Oct04 Nov04 Dec04 Jan05 Feb05 Mar05 Apr05 May05 Jun05 Jul05 results can be compared with those obtained with food density X = 15 Field data Simulated data with only Phyto-C as food resource [Phyto-C]. At Maliakos Gulf, in - Simulated data with POC contribution 10 cluding POC in the diet resulted

(g) in a better fit between simulated W 5 and field data. This area is characterized by low Phyto-C concentra- 0 Oct04 Nov04 Dec04 Jan05 Feb05 Mar05 Apr05 May05 Jun05 Jul05 tions from the middle of February until late April. During this period, Fig. 3. Simulated mussel shell length (L) (top) and fresh tissue mass (W) against Maliakos data (mean ± SD), using phytoplankton carbon biomass (Phyto-C) (X = POC values are higher relative [Phyto-C]; blue line) and both Phyto-C and particulate organic carbon (POC) to Phyto-C and this appears to (Eq. 12; green line) in the mussel diet significantly contribute to mussel growth. On the other hand, POC appears to have no significant 10 role in the M. galloprovincialis diet at Thermaikos Gulf, as in this 5 area Phyto-C is characterized by (cm)

L much weaker variability, with POC concentrations always lower than 0 May95 Jul95 Sep95 Nov95 Jan96 Mar96 May96 Jul96 Phyto-C.

Field data 15 Simulated data with only Phyto-C as food resource Simulated data with POC contribution Comparison between field and 10 simulated data: model (g)

W performance 5

0 As a useful index of the model May95 Jul95 Sep95 Nov95 Jan96 Mar96 May96 Jul96 skill, simulated mussel growth Fig. 4. Simulated mussel shell length (L) (top) and fresh tissue mass (W) against was plotted against field data in Thermaikos data (mean ± SD), using phytoplankton carbon biomass (Phyto-C) Figs. 5 & 6. Points along the x = y (X = [Phyto-C]; blue line) and both Phyto-C and particulate organic carbon (POC) line indicate a perfect fit. In most (Eq. 12; green line) in the mussel diet occasions, points are very close to that line. Moreover, the model −3 values for the 2 areas: Xk = 36 mg C m for Maliakos bias and un biased root-mean-square-deviation −3 Gulf and Xk = 28 mg C m for Thermaikos Gulf; Xk (RMSD) against field data were calculated and not only depends on species but is also site-specific plotted on target diagrams (Jolliff et al. 2009) in

(Troost et al. 2010). The different values of Xk (36 mg Figs. 7 & 8. The marks are very close to the center C m−3 or 0.72 µg chl a l−1 at Maliakos and 28 mg C m−3 of the diagram, indicating a successful simulation. or 0.56 µg chl a l−1 at Thermaikos) that were fitted for The mean model bias, indicated on the y-axis, the 2 study areas can be attributed to differences in shows that referring to the overall mean value, the Phyto-C variability between the 2 environments (see simulated shell length is slightly overestimated (y > ‘Environmental data’ above). These fitted values of 0), while the fresh mass tissue is slightly underesti-

Xk were, as expected, slightly lower compared to mated (y < 0) at Maliakos Gulf and in a very good those found in more productive areas. Casas & agreement with field data at Thermaikos Gulf (y ~ −1 −3 Bacher (2006) found Xk = 3.88 µg l (~194 mg C m ) 0). Additionally, the unbiased RMSD suggests that on the French Mediter ranean shoreline, while Troost the standard deviation of the model is larger (x > 0) −1 −3 et al. (2010) found Xk = 2.23 µg l (~116.5 mg C m ) except for the fresh mass tissue at Thermaikos Gulf in southwest Netherlands. (x < 0). 378 Aquacult Environ Interact 9: 371–383, 2017

8 sitivity (Bacher & Gangnery 2006), Shell length simulation 7 were perturbed by 50 and 100%. 6 In the Thermaikos Gulf simula- 5 tion, where initial R was set at zero, 5 values from 0 to 100 J were 4 adopted. Model runs were exe- 3 Simulation data (cm) 345678cuted with each possible combina- Field data (cm) tion of the 3 parameter values, giv- ing a total of 125 runs. The mean 8 Fresh tissue mass simulation and standard deviation from all 6 model results were then calculated, as shown in Figs. 9 & 10 for the 4 Maliakos and Thermaikos study 2 cases, respectiv ely. Araújo & New Simulation data (g) 0 (2007) demonstrated the advan- 0123456789 tages of an ensemble forecasting in Field data (g) biological models. Instead of select- Fig. 5. Field data against simulation data (stars) at Maliakos Gulf plotted against a ing the best tuning values, a better y = x line procedure is to present a range of possible model states within an Model uncertainty and ensemble forecasting envelope concerning the representative parameteri - zation/ initialization values. The initial values of E and R and the values of the The uncertainty of the model, as represented by the

calibrated parameters (Xk, af, b f) may be considered standard deviation, appears to increase as the mussel relatively unknown. To examine the model’s sen - grows, particularly regarding its wet weight. This sitivity relative to the uncertainty of initialization/ does not indicate a decrease in the model skill, as a calibration, a series of sensitivity simulations were similar increase of standard deviation with growing performed, adopting a representative envelope of mussels was also found in the wet weight field data, 5 different values (Table 5) for each initial value considering that each individual of the farm may grow and calibrated parameter, with the exception of the in a different way, ultimately reaching a different final

preference coefficients af and bf, which did not show weight. This does not apply to the shell length evolu- a significant sensitivity in preliminary tests. Xk was tion, which seems to be a more standard process. It is perturbed by 15 and 30% of its standard value, while also noticeable that a weakness of the model is in effi- initial E and R, to which the model shows less sen - ciently simulating the individual’s production of fresh tissue mass during the period before spawning (from early 8 November 2004 to early Jan- Shell length simulation 6 uary 2005 for Maliakos, and during October 1995 for 4 Thermaikos Gulf). This could 2 imply errors in the simulated

0 reproduction of the individ- Simulation data (cm) 012345678ual that are either related to Field data (cm) the adopted spawning day/ period or to the assumed Fresh tissue mass simulation 10 weight loss due to spawning. According to Van Haren et

5 al. (1994), mussels lose 40 to 70% of their wet weight during spawning. This does not Simulation data (g) 0 0 2 4 6 8 10 12 occur in the presented simu- Field data (g) lations, where weight loss is Fig. 6. Field data against simulation data (stars) at Thermaikos Gulf plotted against a y = x line around 10%. However, if the Hatzonikolakis et al.: DEB mussel model 379

Bias The 2 environments showed differences mostly in terms of Phyto-C and POC fluctuations and maximum values, which has an impact on the diet of M. gallo- 0.8 provincialis. At first, model simulations were performed accounting for only Phyto-C as a food resource for the mussel. In a second approach, available food density was modified to also include POC, (L) aiming to investigate the contribution of POC to Unbiased mussel growth. In this case, following the available lit- -0.8 0 0.8 RMSD (W) erature, it was assumed that M. galloprovincialis as- similates POC only when the density of Phyto-C is not enough for its needs. This was formulated, adopting

different preference coefficients for Phyto-C (af = 0.55) -0.8 and POC (b f = 0.45) in the mussel food density (Eq. 12). The results showed a small contribution of POC at Maliakos Gulf and almost none at Thermaikos Gulf. This is in agreement with Troost et al. (2010), Fig. 7. Target diagram of simulated shell length (L) and fresh mass tissue weight (W) against field data from the Maliakos who found a site-dependent contribution of detritus. Gulf. The model bias is indicated on the y-axis while the un- The values of af and b f could be parameterized in a biased root-mean-square-deviation (RMSD) is indicated on way that would allow POC to have a more significant the x-axis role in the mussel growth. Simulations with higher b f simulation continues for a second or a third year, the (0.55 to 0.8) and lower af (0.45 to 0.2), combined with percentage of wet weight loss increases to 20% on higher values of Xk, showed that the model could pro- subsequent spawning events. duce similar results to those presented; however, this would be in conflict with most of the literature, where phytoplankton is considered the principal food source DISCUSSION for mussels (Williams 1981, Langdon & Newell 1990, Garen et al. 2004). In general, the simulations are sat- A DEB model was developed and tuned against isfactory when considering only Phyto-C as available data from Maliakos and Thermaikos Gulfs to study food for the mussel. Under this assumption, the model the growth of cultured mussel Mytilus galloprovincialis. is simplified, with Xk being the only parameter that has to be tuned. However, the model appears more Bias stable when POC is included in the mussel’s diet. The 2 study areas are very similar with regard to sea surface temperature, and thus differences in the 0.8 Table 5. Parameter values used for the estimation of model uncertainty. Bold numbers are the standard values of initial energy reserves (E), initial energy allocated to development and reproduction (R) and half saturation coefficient (X ) (L) k Unbiased -0.8 0 0.8 –3 (W) RMSD Initial E (J) Initial R (J) Xk (mg C m ) Maliakos Gulf 0 0 25.2 350 150 30.6 -0.8 700 300 36 1050 450 41.4 1400 600 46.8 Thermaikos Gulf 0 0 19.6 Fig. 8. Target diagram of simulated shell length (L) and fresh 175 20 23.8 mass tissue weight (W) against field data from the Ther- 350 50 28 maikos Gulf. The model bias is indicated on the y-axis while 500 80 32.2 the unbiased root-mean-square deviation (RMSD) is indi- 700 100 36.4 cated on the x-axis 380 Aquacult Environ Interact 9: 371–383, 2017

6 (cm) L 4

2 Oct04 Nov04 Dec04 Jan05 Feb05 Mar05 Apr05 May05 Jun05 Jul05

10 (g) W 5

0 Oct04 Nov04 Dec04 Jan05 Feb05 Mar05 Apr05 May05 Jun05 Jul05

Fig. 9. Model uncertainty for the Maliakos simulation. Blue lines: the 125 model runs with each possible combination among the perturbed values of the initial energy reserves (E), reproductive buffer (R) and half-saturation coefficient (Xk) given in Table 5. Red line: computed mean value; black lines: ± SD. Red crosses and bars are for field data (mean ± SD)

5 (cm) L

0 May95 Jul95 Sep95 Nov95 Jan96 Mar96 May96 Jul96

(g) 10 W

0 May95 Jul95 Sep95 Nov95 Jan96 Mar96 May96 Jul96

Fig. 10. Model uncertainty for the Thermaikos simulation. Blue lines: the 125 model runs with each possible combination among the perturbed values of initial energy reserves (E), reproductive buffer (R) and half saturation coefficient (Xk) given in Table 5. Red line: computed mean value; black lines: ± SD. Red crosses and bars are for field data (mean ± SD) growth of cultured mussels may be attributed only text of a climate change scenario investigating the to differences in food resources. Temperature affects effect of global warming on Aegean Sea mussel the growth of the simulated mussel through the farms. temperature dependence k(T), which is multiplied To quantify the uncertainty related to the fitted · · · by each physiological rate (i.e. pa, pc, [pM]). Increas- model parameters (initial values of E and R and Xk), ing the temperature time series by 1°C in the Mali- different values of these parameters were tested and akos Gulf simulation resulted in an increase of a series of simulations was performed with all possi- 0.86% for final shell length and 2.83% for final ble combinations, leading to a representation of the fresh mass tissue. Although this response to temper- DEB model uncertainty. The results showed that in ature does not seem significant for the purpose of most cases, the uncertainty related to the different the present study, it could be interesting in the con- simulations is within the limits of the field data stan- Hatzonikolakis et al.: DEB mussel model 381

dard deviation, suggesting that small perturbations & New 2007) in the DEB model could be used to to the calibrated values of E, R and Xk do not have apply climate change scenarios and investigate a strong influence on model outputs and thus the climate change effects on species. model remains valid. Although the model worked well at the 2 specific In general, the model performed well in simulating study areas and ensemble forecasting provided a the growth of the cultured mussel M. galloprovin- quantification of uncertainties due to parameters and cialis. While the simulation of shell length growth initial value calibrations, the model still suffers from was satisfactory, the agreement between observed some limitations. In the present study, the simulated and simulated weights was not as good, suggesting individual is considered to be representative of the that there is a need for optimization of parameters mussel farm’s mean state. However, one should also related to the weight−length relations, such as the take into account the farm’s population effect. Gener- energy content of reserves (μE) and the shape coeffi- ally, in a predator−prey system the rate of an indi - cient (δm), for which many different estimates can be vidual’s consumption is affected by the density of found in the literature (Casas & Bacher 2006, Van der predators (Kratina et al. 2009). Kratina et al. (2009) Veer et al. 2006, Thomas et al. 2011, Sarà et al. 2012). tested different functional responses, concluding that In the present study, the best fit with the field data those taking into account predator density provide was obtained with parameter values adopted from better results. In the context of the present study, one Casas & Bacher (2006). Representation of model way to take into account the effect of the farm’s pop- uncertainty due to initial E, R and Xk led to a more ulation on individual mussel growth with the DEB reliable simulation, as in most occasions there is no model would be to modify the Hollings Type II func- easy way to estimate those parameters with satisfac- tional response function (f), expressing X and Xk in tory accuracy. More work in this direction needs to terms of food resources per mussel density. This be done in the future, as there is still room for opti- approach could be tested in future work. mization of the DEB parameters. In his work on the Another simplification that can be regarded as a estimation of DEB parameters for bivalve species, limitation of the model is the assumption that M. Van der Veer et al. (2006) concluded that there was a galloprovincialis filtrates phytoplankton and POC of standard error of about 30% on his estimates. Differ- every size. Many studies emphasize the selectivity of ent values can be found among different studies on Mytilus spp. with respect to size and species of the same species; i.e. Troost et al. (2010) and Thomas phytoplankton (Bayne et al. 1987, Raby et al. 1997 et al. (2011) used a fraction of utilized energy spent among others). Other studies (Lehane & Davenport on maintenance/growth κ = 0.45 for M. edulis, while 2006, Prato et al. 2010, Ezgeta-Bali et al. 2012) sug- Picoche et al. (2014) used κ = 0.67. Other relevant gest that Mytilus spp. can consume even zooplank- δ · examples involve m and {pAm}; Sarà et al. (2012) and ton in certain periods and areas. Therefore, in order δ · Rinaldi et al. (2014) used m = 0.2254 and {pAm} = to have a detailed description of mussel diet, food 173.184 J cm−2 d−1 (= 7.216 J cm−2 h−1) for M. gallo- density X should consist of each proxy food (different provincialis, while Casas & Bacher (2006) and Zaldí- size groups of phytoplankton and POC) separately δ · −2 −1 var (2008) used m = 0.25 and {pAm} = 147.6 J cm d , adjusted by a suitable preference weight; an effort which worked better with the presented data. Build- that should be supported by field data diet analyses. ing an envelope of a targeted set of the most sensitive On the other hand, such a model would be more dif- model parameters with different values found in the ficult to tune, and uncertainties due to parameter κ δ · literature (such as , m and {pAm}) could lead to more calibration would be higher. reliable and general ensemble simulations, and also Due to its generic character, the model developed provide an estimate of the model uncertainty re lated in the present study can easily be adapted to simu- to these parameters. This could be strengthened by late the growth of other bivalve species, such as including in the ensemble other bio-energetic indi- native oysters Ostrea edulis and European clams vidual models (such as a SFG model; Brigolin et al. Tapes decussatus, with potential farming interest in 2009 among others). Furthermore, a full description Greek coastal waters. of the model uncertainties should include uncertainty due to environmental forcing, along with uncertain- Acknowledgements. The authors thank George Verriopou- ties due to parameterization and initialization. This los, professor of marine biology at the University of Athens for his helpful advice on biological matters. Data provided complete representation of a DEB model uncertain - for Maliakos are outcomes of the Project ARCHIMIDES I ties could lead to a better understanding of the model −EPEAEK II-EU funded (contract no 10012-00004) ‘Environ- dynamics. Additionally, en semble forecasting (Araújo mental Interactions of the Mussel farming’ (2004–2007). 382 Aquacult Environ Interact 9: 371–383, 2017

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Editorial responsibility: Gianluca Sará, Submitted: November 24, 2016; Accepted: June 26, 2017 Palermo, Italy Proofs received from author(s): September 5, 2017